1. Field of the Invention
The present invention generally relates to a method of generating a free-form surface model based on a reversible rounding operation, a method of generating a lattice polygon model from the generated free-form surface model, a record medium having a program embodied therein for practicing these methods, and a method of transmitting and displaying the free-form surface model. The present invention particularly relates to a method generating a free-form surface model through a perfectly reversible rounding operation where an accurate free-form surface model can be generated.
2. Description of the Related Art
A shape represented by a lattice polygon model is characterized by its simple structure that is easy to design. A lattice polygon model can be turned into a free-form surface model by a rounding operation. Use of the rounding operation makes it possible to readily generate a free-form surface model by designing a lattice polygon model. In the prior art, however, there is no known scheme to reconstruct an original lattice polygon model from a free-form surface model generated therefrom. Once a free-form surface model is generated, the original lattice polygon model cannot be obtained from the data of the generated model shape alone, thereby preventing reuse of the lattice polygon model to create another form.
In a network environment today, transfer and exchange of 3D data are not performed on a frequent basis. A standard representation of 3D shapes that is used when transferring 3-dimensional data over a network is VRML (Virtual Reality Modeling Language). In VRML, data is represented by a set of flat planes that are polygons. A polygon representation has a drawback in that an increase in a level of detail of a represented shape requires an increase in data size. In particular, data that represents many free-form surfaces requires a large number of polygons, resulting in an undesirably large data size. This discourages transfer of data over a network. A further problem is that when polygon-representation data is transferred, a displayed shape has a level of detail that can be decreased but-cannot be increased. In this manner, a 3D shape cannot be represented with sufficient quality if a small data size is used, thereby severely discouraging use of 3D data in a network environment.
In another field of endeavor, 3D-CAD systems used in manufacturing industries use a data-representation scheme that represents a solid model having detailed free-form surface data. Such data representation is now beginning to be supported by standard formats such as IGES (Initial Graphic Exchange Specification) or STEP (Standard for the Exchange of Product Model Data). In the world of CAD, a precise shape-representation scheme called a trimmed free-form surface has been used for the purpose of representing generated free-form surfaces with high accuracy. Such schemes are suitable for highly accurate representation of shape. Because of a required large data size, however, it is difficult to use these schemes in the network environment.
Reversible rounding schemes known to date include those disclosed in: (1) Japanese Patent Laid-open Application No. 9-314697; (2) Atsushi Nakamura, “A Study on Free-form Deformation with Rounding Operation,” a Master's Thesis with Keio University, Graduate School of Media and Governance, 1998; and (3) Yuichiro Chaki, “A Study on Flexible Surface Control by Control Lattice,” a Master's Thesis with Keio University, Graduate School of Media and Governance, 1998. These schemes are not perfect, however, in that there is a requirement, among others, that all surfaces constituting polygons be coplanar.
There is another scheme called a subdivision surface. This scheme generates a pseudo free-form surface model by subdividing a polygon model. This scheme maintains reversibility, but is only a scheme for generating subdivided polygon models for the purpose of display. This scheme is inherently different from a scheme that generates a precise free-form surface model.
The VRML, which is a representation scheme used in the network environment, is based on use of polygons. As previously noted, a polygon-based representation has a drawback in that as an increased level of detail is pursued, data size inevitably increases. If attempt is made to represent a complex shape with a small amount of data, quality of shape representation is degraded, resulting in a lower display quality.